Computational Error and Complexity in Science and Engineering: Computational Error and Complexity

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Elsevier, Mar 4, 2005 - Computers - 260 pages
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The book “Computational Error and Complexity in Science and Engineering pervades all the science and engineering disciplines where computation occurs. Scientific and engineering computation happens to be the interface between the mathematical model/problem and the real world application. One needs to obtain good quality numerical values for any real-world implementation. Just mathematical quantities symbols are of no use to engineers/technologists. Computational complexity of the numerical method to solve the mathematical model, also computed along with the solution, on the other hand, will tell us how much computation/computational effort has been spent to achieve that quality of result. Anyone who wants the specified physical problem to be solved has every right to know the quality of the solution as well as the resources spent for the solution. The computed error as well as the complexity provide the scientific convincing answer to these questions.
Specifically some of the disciplines in which the book will be readily useful are (i) Computational Mathematics, (ii) Applied Mathematics/Computational Engineering, Numerical and Computational Physics, Simulation and Modelling. Operations Research (both deterministic and stochastic), Computing Methodologies, Computer Applications, and Numerical Methods in Engineering.

Key Features:

- Describes precisely ready-to-use computational error and complexity
- Includes simple easy-to-grasp examples wherever necessary.
- Presents error and complexity in error-free, parallel, and probabilistic methods.
- Discusses deterministic and probabilistic methods with error and complexity.
- Points out the scope and limitation of mathematical error-bounds.
- Provides a comprehensive up-to-date bibliography after each chapter.

· Describes precisely ready-to-use computational error and complexity
· Includes simple easy-to-grasp examples wherever necessary.
· Presents error and complexity in error-free, parallel, and probabilistic methods.
· Discusses deterministic and probabilistic methods with error and complexity.
· Points out the scope and limitation of mathematical error-bounds.
· Provides a comprehensive up-to-date bibliography after each chapter.
 

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Contents

1 Introduction
1
Precisely What Why and How
25
What Why and How
63
4 Errors and Approximations in Digital Computers
95
5 Error and Complexity in Numerical Methods
147
6 Error and Complexity in ErrorFree Parallel and Probabilistic Computations
195
Index
237
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Page 12 - Let us imagine the operations performed by the computer to be split up into 'simple operations' which are so elementary that it is not easy to imagine them further divided. Every such operation consists of some change of the physical system consisting of the computer and his tape. We know the state of the system if we know the sequence of symbols on the tape, which of these are observed by the computer (possibly with a special order), and the state of mind of the computer.

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